Is it possible to insert a keyframe to a metaball element?
With obj.keyframe_insert you are adding a keyframe for the object, not the element.

To set keyframes for elem2 you want to use elem2.keyframe_insert

elem2.co = Vector((2,0,0))
elem2.keyframe_insert(data_path="co", frame = 10)

elem2.co = Vector((0,2,0))
elem2.keyframe_insert(data_path="co", frame = 100)